On linear structure and phase rotation invariant properties ofblock M-PSK modulation codes

Two important structural properties of block M(=2^' )-ary PSK modulation codes, linear structure and phase symmetry, are investigated. An M-ary modulation code is first represented as a code with symbols from the integer group S_M-PSK=(0,1,2,---,M-1) under modulo-M addition. Then the linear structure of block M-PSK modulation codes over S_M-PSK with respect to modulo- M vector addition is defined, and conditions are derived under which a block M-PSK modulation code is linear. Once the linear structure is developed, the phase symmetry of block M-PSK modulation codes is studied. In particular, a necessary and sufficient condition for a block M-PSK modulation code that is linear as a binary code to be invariant under 2^h/180°M phase rotation, for 1⩽h⩽l is derived. Finally, a list of short 8-PSK and 16-PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant     

A simple derivation of the power spectrum of full-response CPM andsome of its properties

Using a new representation for continuous-phase modulated (CPM) signals, it is shown how a closed-form expression for the power spectral density of full-response M-ary CPM with modulation index J /M can be obtained by straightforward computations. This result is used to provide an explanation of the fact that this power spectral density depends only on J and not on M     

Combined coded/multi-h CPFSK signaling

A continuous-phase frequency-shift-keying (CPFSK) signaling technique is suggested that combines convolutional encoding and multi- h signaling. In contrast to regular multi-h signaling, this technique changes the modulation index in a preselected pattern in order to maximize the minimum Euclidean distance. A rate-1/2 convolutional encoder along with a 2-h quaternary CPFSK modulator which uses two fixed modulation indexes is considered. Minimum Euclidean distances are calculated corresponding to the best encoder/mapper combinations for different modulation index patterns at attractive pairs of modulation indexes. Numerical results obtained for encoder memory lengths of one and two are used to illustrate that the minimum Euclidean distance of coded CPFSK signals can be significantly increased by combining with multi-h signaling. Modulation index patterns which perform significantly better than regular multi-h signals are determined. An error event analysis over the additive-white-Gaussian noise channel is carried out to investigate the actual error rate performance and to verify the theoretical results     

Limiter-discriminator detection of a coherent optical heterodyneM-ary CPFSK receiver

The performance of a coherent optical M-ary continuous-phase frequency-shift-keying (CPFSK) receiver using limiter-discriminator (L-D) detection is investigated. It is shown that L-D detection of CPFSK optical signals offers the best performance for a large normalized IF beat spectral linewidth, ΔνT. When the modulation index is unity, the receiver is immune to laser phase noise and can produce (M/4) exp (-SNR) symbol error probability, which may be considered as the upper bound if the optimal modulation index is used (SNR is the signal-to-noise ratio per symbol). Optimum modulation indexes are 0.8 and 1 at ΔνT=1% and ΔνT=2%, respectively, for M=4, 8, and 16     

Error-correcting codes and nonlinear diversity combining againstworst case partial-band noise jamming of frequency-hopping MFSK systems

Error probability analyses are performed for a coded M-ary frequency-shift keying system (MFSK) using L hops per M-ary word frequency-hopping spread-spectrum waveforms transmitted over a partial-band Gaussian noise jamming channel. The bit error probabilities are obtained for a square-law adaptive gain control receiver with forward-error-control coding under conditions of worst-case partial-band noise jamming. Both thermal noise and jamming noise are included in the analyses. Performance curves are obtained for both block codes and convolutional codes with both binary and M-ary channel modulations. The results show that thermal noise cannot be neglected in the analysis if correct determinations of the optimum order of diversity and the worst-case jamming fraction are to be obtained. It is shown that the combination of nonlinear combining, M -ary modulation, and forward-error-control coding is effective against worst-case partial-band noise jamming     

Pseudo-analog speech transmission in mobile radio communicationsystems

A low-complexity pseudo-analog speech transmission scheme is proposed for portable communications. It uses a speech coder based on adaptive differential pulse code modulation (ADPCM) in combination with a multilevel digital modulation technique such as M-ary DPSK or M-ary FSK and features low quantization noise, bandwidth efficiency, and robustness to transmission errors. A nonsymmetric M -ary DPSK scheme called skewed M-ary DPSK is proposed to enhance the noisy channel performance. Comparison to conventional analog FM and a digital speech transmission scheme using adaptive predictive coding and forward error correction (FEC) based on convolutional coding shows that the pseudo-analog system has the best objective signal-to-noise ratio performance under most channel conditions. Informal subjective evaluations rate the digital system superior to the pseudo-analog scheme for bad channels and conversely for good channels. It is concluded that the pseudo-analog system can be designed with low delay and high speech quality for good channels with high spectral efficiency     

Repeated convolutional codes for high-error-rate channels

An error-correction scheme for an M-ary symmetric channel (MSC) characterized by a large error probability p_e is considered. The value of p_e can be near, but smaller than, 1-1/M, for which the channel capacity is zero, such as may occur in a jamming environment. The coding scheme consists of an outer convolutional code and an inner repetition code of length m that is used for each convolutional code symbol. At the receiving end, the m inner code symbols are used to form a soft-decision metric, which is passed to a soft-decision decoder for the convolutional code. The effect of finite quantization and methods to generate binary metrics for M>2 are investigated. Monte Carlo simulation results are presented. For the binary symmetric channel (BSC), it is shown that the overall code rate is larger than 0.6R₀, where R₀ is the cutoff rate of the channel. New union bounds on the bit error probability for systems with a binary convolutional code on 4-ary and 8-ary orthogonal channels are presented. For a BSC and a large m, a method is presented for BER approximation based on the central limit theorem     

Spread-spectrum multiple-access performance of orthogonal codes forindoor radio communications

Direct-sequence spread spectrum, with its inherent resistance to multipath, is a promising technique for indoor wireless communication. To allow multiple users within a limited bandwidth, code division multiple access (CDMA) is needed. The bandwidth efficiency of M-ary CDMA systems in fading multipath indoor radio channels is analyzed. It is shown that M-ary signaling improves the bandwidth efficiency significantly when compared to binary signaling     

Correlatively encoded multi-h signals

A correlatively encoded multi-h CPFSK signaling technique which performs significantly better than partial response multi-h signaling is introduced. Numerical results presented for binary 2- h signaling indicate that correlatively encoded 2-h signals can achieve significant gains over both constant h signals and partial response 2-h signals     

Performance of fast frequency hopped noncoherent MESK witha fixed hop rate under worst case jamming

The performance of fast-frequency-hopped M-ary frequency-shift keying with a fixed hop rate is evaluated, utilizing the Chernoff union bound method. The performance criterion used is a throughput measure i.e., an information rate sustained by a system for a given bit error rate, normalized by the hop rate. Both uncoded and coded systems are considered. It is shown using the cutoff rate argument that coding can provide a few dB gain in throughput. This is confirmed by the performance evaluation of various convolutional and block codes. Both partial-band noise jamming and multitone jamming with one tone per M -ary band are considered. Jamming parameters are assumed to be the worst case against the coding channel. Determination of the optimum M is also addressed     

Frequency-hopped multiple access communications with coding andside information

The authors consider frequency-hopped spread-spectrum multiple-access communications using M-ary modulation and error-correction coding. The major concerns are multiple-access interference and the network capacity in terms of the number of users that can transmit simultaneously for a given level of codeword error probability. Block coding is studied in detail. The authors first consider the use of Q-ary Reed-Solomon (RS) codes in combination with M-ary modulation with mismatched alphabets so that Q>M. It is shown that the network capacity is drastically reduced in comparison with the system with matched alphabets. As a remedy, the use of matched M-ary BCH codes is proposed as an alternative to mismatched RS codes. It is shown that when the number of users in the system is large, a BCH code outperforms an RS code with a comparable code rate and decoding complexity. The authors consider the use of a robust technique for generation of reliable side information based on a radio-threshold test. They analyze its performance in conjunction with MFSK and error-erasure correction decoding. It is shown that this nonideal ratio-threshold method can increase the network capacity in comparison with the system with perfect side information     

Offset DPSK with differential phase detector in satellite mobilechannel with narrow-band receiver filter

An expression is derived for the error probability of M-ary offset differential phase-shift keying (DPSK) with the differential phase detector and narrowband receiver filter in the satellite mobile (Rician) channel, which includes as special cases the Gaussian and land mobile (Rayleigh) channels. The error probability is computed as a function of various system parameters for M=2, 4, and 8 symbols and third-order Butterworth receiver filter. Both symmetric and conventional DPSK systems are considered. The optimal normalized bandwidth is close to 1.0. Symmetric and conventional DPSK differ significantly in error probability only for M=2 and in the lower range filter bandwidth. In most cases, symmetric DPSK outperforms conventional DPSK. This was particularly noted when the time delay between the specular and diffused signal components was taken into account     

On repeated-root cyclic codes

A parity-check matrix for a q-ary repeated-root cyclic code is derived using the Hasse derivative. Then the minimum distance of a q-ary repeated-root cyclic code is expressed in terms of the minimum distance of a certain simple-root cyclic code. With the help of this result, several binary repeated-root cyclic codes of lengths up to n=62 are shown to contain the largest known number of codewords for their given length and minimum distance. The relative minimum distance d_min/n of q-ary repeated-root cyclic codes of rate r⩾R is proven to tend to zero as the largest multiplicity of a root of the generator g(x) increases to infinity. It is further shown that repeated-root cycle codes cannot be asymptotically better than simple-root cyclic codes     

Sliding-block coding for input-restricted channels

Work on coding arbitrary sequences into a constrained system of sequences (called a sofic system) is presented. Such systems model the input constraints for input-restricted channels (e.g., run-length limits and spectral constraints for the magnetic recording channel). In this context it is important that the code be noncatastrophic to ensure that the decoder has limited error propagation. A constructive proof is given of the existence of finite-state invertible noncatastrophic codes from arbitrary n-ary sequences to a sofic system S at constant rate p:q provided only that Shannon's condition (p/q)⩽(h/log n) is satisfied, where h is the entropy of the system S. If strict inequality holds or if equality holds and S satisfies a natural condition called `almost of finite type' (which includes the systems used in practice), a stronger result is obtained, namely, the decoders can be made `state-independent' sliding-block. This generalizes previous results. An example is also given to show that the stronger result does not hold for general sofic systems     

Defining, designing, and evaluating digital communication systems

The fundamental relationships in defining, designing, and evaluating digital communication system performance are reviewed. The concept of bandwidth-limited and power-limited systems and how such conditions influence the design when the choices are confined to M -ary phase-shift keying (MPSK) and M-ary frequency-shift keying (MFSK) modulation are examined. The definitions and computations involved in transforming from data bits to channel bits to symbols to chips are discussed. It is suggested that since most digital communication systems share these concepts, understanding them should enable one to evaluate other such systems in a similar way     

Optimisation of parameters in an MFSK transmission system

An optimisation technique for maximising the information throughput of an M-ary frequency-shift keyed (MFSK) transmission system is described. An upper bound for the error-free throughput of the system in the presence of additive white Gaussian noise (AWGN) for different numbers of tones, M, is derived. From this, the optimum range for M can be identified     

Asymptotic performance of M-ary orthogonal modulation ingeneralized fading channels

The asymptotic (M→∞) probability of symbol error P_e,_m for M-ary orthogonal modulation in a Nakagami-m fading channel is given by the incomplete gamma function P(m, mx) where x=In 2/(E_b/N₀) and E_b is the average energy per bit. For large signal-to-noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of E_b/N₀. These channels exist for all m⩾1/2. The special case of m=1 corresponds to Rayleigh fading, an inverse linear channel     

Performance analysis of RS-coded M-ary FSK forfrequency-hopping spread spectrum mobile radios

Decoding performance of Reed-Solomon (RS) coded M-ary FSK with noncoherent detection in a frequency-hopping spread spectrum mobile radio channel is theoretically analyzed. Exact formulas and an approximate one for evaluating word error rates (WERs) of error correction and error-and-erasure correction schemes on decoding the RS codes are derived. It is shown that with K symbol erasure and C symbol error detection, RS coded M-ary FSK achieves the equivalent diversity order of (K+1)(C+1)